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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 536 · 40 questions
TalentJR

How to solve it (Across, up, Pythagoras): Distance: across = difference of the x values, up = difference of the y values; distance = √(across² + up²). Midpoint = ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2). Quadrants by signs: (+, +) first, (−, +) second, (−, −) third, (+, −) fourth.

NameDateTime takenScore ___ / 40
  1. 1.What is the distance between the points (9, 15) and (15, 7)? (a) 14 (b) 11 (c) 10 (d) 100
  2. 2.What is the distance between the points (8, 2) and (23, 10)? (a) 17 (b) 23 (c) 18 (d) 289
  3. 3.What is the distance between the points (1, 7) and (6, 19)? (a) 169 (b) 14 (c) 17 (d) 13
  4. 4.In which quadrant does the point (5, 6) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  5. 5.What is the midpoint of the line joining (3, 7) and (5, 11)? (a) (4, 9) (b) (1, 2) (c) (9, 4) (d) (8, 18)
  6. 6.What is the midpoint of the line joining (4, 0) and (6, 12)? (a) (6, 5) (b) (5, 6) (c) (10, 12) (d) (1, 6)
  7. 7.What is the distance between the points (2, 9) and (8, 1)? (a) 11 (b) 14 (c) 100 (d) 10
  8. 8.In which quadrant does the point (−4, 1) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  9. 9.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 11 (c) 14 (d) 100
  10. 10.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 17 (c) 23 (d) 289
  11. 11.What is the distance between the points (1, 2) and (9, 8)? (a) 11 (b) 14 (c) 10 (d) 100
  12. 12.In which quadrant does the point (−6, 1) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  13. 13.What is the midpoint of the line joining (2, 3) and (6, 11)? (a) (7, 4) (b) (8, 14) (c) (4, 7) (d) (2, 4)
  14. 14.What is the distance between the points (1, 10) and (5, 7)? (a) 5 (b) 6 (c) 7 (d) 25
  15. 15.What is the midpoint of the line joining (6, 12) and (18, 10)? (a) (24, 22) (b) (6, 1) (c) (11, 12) (d) (12, 11)
  16. 16.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 289 (c) 17 (d) 23
  17. 17.What is the midpoint of the line joining (2, 7) and (6, 17)? (a) (8, 24) (b) (12, 4) (c) (2, 5) (d) (4, 12)
  18. 18.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 17 (c) 169 (d) 13
  19. 19.What is the distance between the points (0, 7) and (5, 19)? (a) 14 (b) 17 (c) 169 (d) 13
  20. 20.What is the distance between the points (0, 12) and (8, 6)? (a) 100 (b) 14 (c) 10 (d) 11
  21. 21.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 10 (c) 11 (d) 100
  22. 22.What is the midpoint of the line joining (2, 22) and (12, 10)? (a) (16, 7) (b) (5, 6) (c) (7, 16) (d) (14, 32)
  23. 23.In which quadrant does the point (1, −9) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  24. 24.In which quadrant does the point (−6, 6) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  25. 25.What is the midpoint of the line joining (1, 18) and (7, 6)? (a) (8, 24) (b) (12, 4) (c) (4, 12) (d) (3, 6)
  26. 26.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 20 (c) 400 (d) 28
  27. 27.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 6 (c) 25 (d) 5
  28. 28.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 17 (c) 13 (d) 169
  29. 29.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 225 (c) 15 (d) 16
  30. 30.What is the midpoint of the line joining (2, 2) and (10, 0)? (a) (6, 1) (b) (12, 2) (c) (1, 6) (d) (4, 1)
  31. 31.What is the midpoint of the line joining (8, 9) and (16, 17)? (a) (13, 12) (b) (12, 13) (c) (24, 26) (d) (4, 4)
  32. 32.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 225 (c) 16 (d) 15
  33. 33.What is the distance between the points (4, 8) and (28, 15)? (a) 26 (b) 25 (c) 31 (d) 625
  34. 34.What is the distance between the points (5, 15) and (11, 7)? (a) 10 (b) 100 (c) 11 (d) 14
  35. 35.What is the distance between the points (0, 0) and (8, 15)? (a) 289 (b) 23 (c) 17 (d) 18
  36. 36.What is the distance between the points (4, 8) and (16, 24)? (a) 21 (b) 20 (c) 28 (d) 400
  37. 37.What is the midpoint of the line joining (8, 9) and (14, 15)? (a) (12, 11) (b) (22, 24) (c) (11, 12) (d) (3, 3)
  38. 38.What is the midpoint of the line joining (4, 6) and (16, 18)? (a) (20, 24) (b) (12, 10) (c) (6, 6) (d) (10, 12)
  39. 39.What is the midpoint of the line joining (4, 17) and (16, 7)? (a) (20, 24) (b) (6, 5) (c) (12, 10) (d) (10, 12)
  40. 40.What is the distance between the points (8, 8) and (14, 16)? (a) 100 (b) 10 (c) 11 (d) 14

Answer key

  1. 10
  2. 17
  3. 13
  4. First quadrant
  5. (4, 9)
  6. (5, 6)
  7. 10
  8. Second quadrant
  9. 10
  10. 17
  11. 10
  12. Second quadrant
  13. (4, 7)
  14. 5
  15. (12, 11)
  16. 17
  17. (4, 12)
  18. 13
  19. 13
  20. 10
  21. 10
  22. (7, 16)
  23. Fourth quadrant
  24. Second quadrant
  25. (4, 12)
  26. 20
  27. 5
  28. 13
  29. 15
  30. (6, 1)
  31. (12, 13)
  32. 15
  33. 25
  34. 10
  35. 17
  36. 20
  37. (11, 12)
  38. (10, 12)
  39. (10, 12)
  40. 10

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